Relative polynomial closure and monadically Krull monoids of integer-valued polynomials

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Let D be a Krull domain and Int(D) the ring of integer-valued polynomials on D. For any f∈Int(D), we explicitly construct a divisor homomorphism from [[f]], the divisor-closed submonoid of Int(D) generated by f, to a finite sum of copies of (N0,+). This implies that [[f]] is a Krull monoid. For V a discrete valuation domain, we give explicit divisor theories of various submonoids of Int(V). In the process, we modify the concept of polynomial closure in such a way that every subset of D has a finite polynomially dense subset . The results generalize to Int(S,V), the ring of integer-valued polynomials on a subset, provided S does not have isolated points in v-adic topology
Original languageEnglish
Title of host publicationMultiplicative Ideal Theory and Factorization Theory
Subtitle of host publicationCommutative and Non-commutative Perspectives
EditorsScott Chapman, Marco Fontana, Alfred Geroldinger, Bruce Olberding
PublisherSpringer International Publishing AG
ISBN (Electronic)978-3-319-38855-7
ISBN (Print)978-3-319-38853-3
Publication statusPublished - 2016

Publication series

Name Springer Proceedings in Mathematics & Statistics
ISSN (Print)2194-1009

ASJC Scopus subject areas

  • Algebra and Number Theory

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


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